Question

How do you simplify `(sqrt2-3)(sqrt6+5)`?

Answer 1

See a solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(sqrt(2)) - color(red)(3))(color(blue)(sqrt(6)) + color(blue)(5))` becomes:

`(color(red)(sqrt(2)) xx color(blue)(sqrt(6))) + (color(red)(sqrt(2)) xx color(blue)(5)) - (color(red)(3) xx color(blue)(sqrt(6))) - (color(red)(3) xx color(blue)(5))`

`sqrt(color(red)(2) * color(blue)(6)) + 5sqrt(2) - 3sqrt(6) - 15`

`sqrt(12) + 5sqrt(2) - 3sqrt(6) - 15`

`sqrt(4 * 3) + 5sqrt(2) - 3sqrt(6) - 15`

`sqrt(4)sqrt(3) + 5sqrt(2) - 3sqrt(6) - 15`

`2sqrt(3) + 5sqrt(2) - 3sqrt(6) - 15`